An obstacle problem with gradient term and asymptotically linear reaction

Abstract

We will consider the following obstacle problem (EQUATION PRESANT) with the condition that ub ≥ ψ a.e in ω. Under suitable condition relating g, h and q, we show the existence of a solution for all f ε L1 (W). The main feature is, assuming that g(x, s) is asymptotically linear as |s| → ± ∞ and independently of the values of (EQUATION PRESANT) to obtain a solution for all X > 0 and f ε L1(ω). In this sense we could say that the first order term break down any resonant effect.